**5. Optimization process**

The authors [14, 28] describe the operation of the sugarcane harvester, which can be categorized into whole stalk harvesters and chopper harvesters. The sugarcane harvester machines perform the basal cutting, promote the cleaning of sugarcane and chop the stalks into 15–40 cm billets, unloading them onto a transshipment (**Figure 5**). Additionally, the sugarcane is deliv-

The mechanized harvesting of the sugarcane is carried out annually and each machine cuts approximately 80 tons per hour. Depending on the number of hours worked, it can cut annu-

Thailand is the second largest exporter and the fifth largest sugarcane producer in the world. However, most sugarcane farming is family business, hence sugarcane is cultivated in a small area, which makes mechanized harvesting unfeasible and promotes low productivity [28, 29]. According to Pongpat et al. [23], despite the great importance of sugarcane to Thailand's economy, the population has been aging and it has been difficult to meet the significant market demand using only manual harvesting. It is necessary to review the concepts and apply new

In Cuba, sugarcane is considered the second largest source of economy, has hundreds of mills and produces millions of tons of sugar per year; however for this, the integrated harvesting,

Sugarcane has a great economic importance in Australia. According to Higgins and Davies [31], in this country, the sugarcane is mostly concentrated in the northeast, and the cut begins in the winter and goes until the end of spring, when the highest percentage of sucrose

**Figure 5.** Transshipment to aid the transport of sugarcane from the plot to the truck or train. Credit: Luiz Carlos Dalben.

ered to a train or a truck and transported to the processing center.

investments in the mechanization of harvesting in this country.

transshipment and loading system work efficiently [30].

is concentrated.

212 Sugarcane - Technology and Research

ally between 50,000 and 150,000 tons per harvester [20].

Investments in technology have grown considerably in developed and developing countries, mainly investments in technologies aimed at agricultural machinery, including sugarcane harvesting machine. Due to these investments, the machines have become more agile and productive, promoting a considerable increase harvesting yields, and consequently forcing managers to make faster decisions during the process of mill management. Therefore, many studies were directed towards the development of optimization mathematical models as a way to assist managers in decision-making.

### **5.1. Mathematical models**

Since the 1970s, many mathematical models have been developed aiming to optimize the mechanical harvesting process of sugarcane

In 1977, Gentil and Ripoli [35] analyzed and simulated the mechanized harvesting system, transport and additionally, the reception of sugarcane in the mills. The logistics of transportation and harvesting of the sugarcane were optimized aiming to reduce the time involved in the harvesting process and the number of vehicles (harvesters and trucks). Despite the computational limitations, promising results were obtained, considering the dimensions of the problems of this time.

In 1982, Singh and Abeygoonawardana [36] developed an optimization model for the harvesting and transport of sugarcane, aiming to optimize the number of trucks for the transportation of harvested sugarcane in mills in Thailand.

In 1994, Singh and Pathak [37] presented an optimization model-based decision support system and simulation of the harvesting operation, aiming to minimize harvesting costs and aid the optimal management decision-making for the mechanized harvesting of sugarcane.

In 1995, Semenzato [38] used a heuristic to simulate the sugarcane harvesting, aiming to assist the decision maker to optimize cutting, loading, transport and discharge time. The results achieved helped in making optimized decisions aiming at the organization and use of scarce resources.

In 1999, Askita et al. [39] developed a scheduling algorithm called SFSW (Stochastic Farm Work Scheduling Algorithm based on Short Range Weather Variation) to assist Japan's sugarcane industry in determining the optimal daily amount of sugarcane to be harvested and deciding which fields to perform the operation of harvest. This algorithm was considered quite promising when was compared to real practices.

In 2008, Salassi and Barker [46] developed a study aiming to reduce costs and minimize harvesting time. In this way, a mathematical programming model was developed, which pro-

Mathematical Optimization Models in the Sugarcane Harvesting Process

http://dx.doi.org/10.5772/intechopen.71530

215

In 2009, Jena and Aragão [47] proposed an integer linear programming model to optimize harvesting. In order to facilitate the resolution of the problem, heuristic initial solutions were obtained and exact methods were applied with the use of CPLEX and other software, obtaining an improvement of almost 25% in the total average of cane production. The authors rec-

In 2010, Scarpari and Beauclair [9] also used linear programming and the General Algebraic Modeling System (GAMS) software to maximize profit and harvesting time for sugarcane.

In 2012, Stray et al. [48] formulated a model of optimization based on traveling salesman problem aiming to determine an optimal planning of the sugarcane harvesting involving large number of fields and extensive areas of planting. The researchers concluded that the decision support system provides practical support for sugarcane harvesting; however, even then, numerous

In 2013, Silva et al. [49] developed and applied a Multi-Choice Mixed Integer Goal Programming Model (MCMIGP) for a real problem of production planning in a sugarcane mill, extending to mechanized harvesting. The authors argue that mathematical techniques are good tools to assist power plant managers in making decisions. Sethanan et al. [50] presented an optimization model applied to sugarcane harvesting aiming to maximize sugar production in the harvest period. The authors presented a heuristic to schedule the sugarcane harvesting and a Tabu Search algorithm to optimize production. The results showed an improvement average of 16.38% in sugar production. Jena and Poggi [8] presented an optimization model for tactical and operational planning such that the total sugar content in the harvested sugarcane is maximized. The model was solved using heuristic techniques and approached Lagrangian relaxation or Benders decomposition.

In 2014, Florentino and Pato [5] presented a bi-objective binary linear programming model for sugarcane variety selection and harvesting residual biomass utilization. The computational experiment showed a high quality of the proposed multiobjective Genetic Algorithm and a low computational time. The authors concluded that the mathematical techniques could aid the managers of mills in the strategic planning process of productive activities of the sugarcane. Silva and Marins [51] proposed a Fuzzy Goal Programming (FGP) model to optimize storage and transport logistics of sugarcane involving uncertainties in the agricultural process of sugar and ethanol production. The results indicated that the presented methodology could assist the managers in the decision making, mainly to the processes related to the harvesting,

In 2015, Silva et al. [52] proposed a Revised Multi-Choice Goal Programming (RMCGP-LHS) model to address uncertainty in sugarcane harvesting planning, production planning and energy cogeneration for a sugarcane mill. The model addresses the agricultural and industrial stages, allowing the decisions to be taken within a weekly planning horizon, including the process of variety selecting of the sugarcane to be planted, the design of the cutting front and the agricultural logistics, as well as the choice of the production process of sugar and ethanol.

vided the ideal harvest time under different waiting times.

researches are needed in this area.

transshipment and transportation of the sugarcane.

ommended the use of mathematical techniques for this type of problem.

In 2000, Díaz and Perez [30] considered that to optimize the harvesting and transportation of sugarcane, involving the cutting and loading of the truck is a complex task. Therefore, these authors proposed a computational simulation aimed at the optimization of sugarcane harvesting and transportation. The results found contributed to the development of optimal planning of sugarcane processes.

In 2001, Arjona et al. [40] observed some problems in Mexican sugar-energy sector related to the underutilized machines and difficulties presented by farmers to plan the sugarcane harvesting. These authors developed a computational simulation of the harvesting, transportation and sugarcane processing systems, aiming to aid managers to plan and evaluate actions with a computational tool. The results of this research allowed the correction of the problems underutilization of machinery and the minimization of costs, fuels and processing time of sugarcane.

In 2002, Higgins [41] proposed an integer linear programming model to optimize the number of harvesters to be used at five Australian mills. The author describes the great importance and benefits that mathematical modeling can promote to power mills. Higgins and Muchow [42], in 2003, also explored operational research techniques to increase productivity and profit in sugarcane production and harvesting.

In 2005, Higgins and Davies [43] emphasized the complexity of mechanized harvesting and transportation in the sugar-energy sector. They proposed a stochastic model to evaluate scenarios of cost reduction in mechanized harvesting and transportation. The results allowed to obtain a more efficient transportation service and with greater benefit to the harvest. Jiao et al. [44] proposed a linear programming model to improve crop planning in order to optimize the amount of cane to be cut per farm and the sugar content. As a result, a software called SugarMax was introduced with the purpose of assisting in decision-making.

In 2006, Higgins [4] proposed a mixed integer linear programming model with the objective of reducing the queuing time of the trucks and optimizing the harvesting process. The computational tests were performed using the GAMS software, OSL and heuristic techniques. Milan et al. [45] studied the transport of sugarcane, involving numerous variables and constraints, such as decisions of the continuous milling, harvesting machining, number of vehicles used to transport sugarcane and available routes. The model was designed to minimize transport cost and harvest limitation.

In 2007, Grunow et al. [32] investigated the safety stock of sugarcane to be used as raw material for sugar production. The problems of cultivating farms, harvesting, dispatching and harvesting equipment were analyzed. A mixed integer linear programming (MILP) model was proposed for the mechanized harvest planning, optimizing the weekly milling of sugarcane and the amount of sucrose and allowing a more detailed harvest schedule with small sucrose losses.

In 2008, Salassi and Barker [46] developed a study aiming to reduce costs and minimize harvesting time. In this way, a mathematical programming model was developed, which provided the ideal harvest time under different waiting times.

In 1999, Askita et al. [39] developed a scheduling algorithm called SFSW (Stochastic Farm Work Scheduling Algorithm based on Short Range Weather Variation) to assist Japan's sugarcane industry in determining the optimal daily amount of sugarcane to be harvested and deciding which fields to perform the operation of harvest. This algorithm was considered

In 2000, Díaz and Perez [30] considered that to optimize the harvesting and transportation of sugarcane, involving the cutting and loading of the truck is a complex task. Therefore, these authors proposed a computational simulation aimed at the optimization of sugarcane harvesting and transportation. The results found contributed to the development of optimal

In 2001, Arjona et al. [40] observed some problems in Mexican sugar-energy sector related to the underutilized machines and difficulties presented by farmers to plan the sugarcane harvesting. These authors developed a computational simulation of the harvesting, transportation and sugarcane processing systems, aiming to aid managers to plan and evaluate actions with a computational tool. The results of this research allowed the correction of the problems underutilization of machinery and the minimization of costs, fuels and processing time of sugarcane. In 2002, Higgins [41] proposed an integer linear programming model to optimize the number of harvesters to be used at five Australian mills. The author describes the great importance and benefits that mathematical modeling can promote to power mills. Higgins and Muchow [42], in 2003, also explored operational research techniques to increase productivity and profit

In 2005, Higgins and Davies [43] emphasized the complexity of mechanized harvesting and transportation in the sugar-energy sector. They proposed a stochastic model to evaluate scenarios of cost reduction in mechanized harvesting and transportation. The results allowed to obtain a more efficient transportation service and with greater benefit to the harvest. Jiao et al. [44] proposed a linear programming model to improve crop planning in order to optimize the amount of cane to be cut per farm and the sugar content. As a result, a software called

In 2006, Higgins [4] proposed a mixed integer linear programming model with the objective of reducing the queuing time of the trucks and optimizing the harvesting process. The computational tests were performed using the GAMS software, OSL and heuristic techniques. Milan et al. [45] studied the transport of sugarcane, involving numerous variables and constraints, such as decisions of the continuous milling, harvesting machining, number of vehicles used to transport sugarcane and available routes. The model was designed to minimize transport

In 2007, Grunow et al. [32] investigated the safety stock of sugarcane to be used as raw material for sugar production. The problems of cultivating farms, harvesting, dispatching and harvesting equipment were analyzed. A mixed integer linear programming (MILP) model was proposed for the mechanized harvest planning, optimizing the weekly milling of sugarcane and the amount of sucrose and allowing a more detailed harvest schedule

SugarMax was introduced with the purpose of assisting in decision-making.

quite promising when was compared to real practices.

planning of sugarcane processes.

214 Sugarcane - Technology and Research

in sugarcane production and harvesting.

cost and harvest limitation.

with small sucrose losses.

In 2009, Jena and Aragão [47] proposed an integer linear programming model to optimize harvesting. In order to facilitate the resolution of the problem, heuristic initial solutions were obtained and exact methods were applied with the use of CPLEX and other software, obtaining an improvement of almost 25% in the total average of cane production. The authors recommended the use of mathematical techniques for this type of problem.

In 2010, Scarpari and Beauclair [9] also used linear programming and the General Algebraic Modeling System (GAMS) software to maximize profit and harvesting time for sugarcane.

In 2012, Stray et al. [48] formulated a model of optimization based on traveling salesman problem aiming to determine an optimal planning of the sugarcane harvesting involving large number of fields and extensive areas of planting. The researchers concluded that the decision support system provides practical support for sugarcane harvesting; however, even then, numerous researches are needed in this area.

In 2013, Silva et al. [49] developed and applied a Multi-Choice Mixed Integer Goal Programming Model (MCMIGP) for a real problem of production planning in a sugarcane mill, extending to mechanized harvesting. The authors argue that mathematical techniques are good tools to assist power plant managers in making decisions. Sethanan et al. [50] presented an optimization model applied to sugarcane harvesting aiming to maximize sugar production in the harvest period. The authors presented a heuristic to schedule the sugarcane harvesting and a Tabu Search algorithm to optimize production. The results showed an improvement average of 16.38% in sugar production. Jena and Poggi [8] presented an optimization model for tactical and operational planning such that the total sugar content in the harvested sugarcane is maximized. The model was solved using heuristic techniques and approached Lagrangian relaxation or Benders decomposition.

In 2014, Florentino and Pato [5] presented a bi-objective binary linear programming model for sugarcane variety selection and harvesting residual biomass utilization. The computational experiment showed a high quality of the proposed multiobjective Genetic Algorithm and a low computational time. The authors concluded that the mathematical techniques could aid the managers of mills in the strategic planning process of productive activities of the sugarcane. Silva and Marins [51] proposed a Fuzzy Goal Programming (FGP) model to optimize storage and transport logistics of sugarcane involving uncertainties in the agricultural process of sugar and ethanol production. The results indicated that the presented methodology could assist the managers in the decision making, mainly to the processes related to the harvesting, transshipment and transportation of the sugarcane.

In 2015, Silva et al. [52] proposed a Revised Multi-Choice Goal Programming (RMCGP-LHS) model to address uncertainty in sugarcane harvesting planning, production planning and energy cogeneration for a sugarcane mill. The model addresses the agricultural and industrial stages, allowing the decisions to be taken within a weekly planning horizon, including the process of variety selecting of the sugarcane to be planted, the design of the cutting front and the agricultural logistics, as well as the choice of the production process of sugar and ethanol. The objectives of this model are to obtain information to harvest the sugarcane in the period closest to the maximum sucrose content; minimize agro-industrial costs and maximize the production of sugar and ethanol and the sale of energy. Neungmatcha and Sethanan [53] carried out studies on optimum planning of the mechanized harvesting route in order to improve transportation. These authors proposed a mixed integer model aiming to increase profits and reduce costs through the better supply of sugarcane and more efficient mechanized harvesting and transportation. Kittilertpaisan and Pathumnakul [54] studied problems related to the mechanized harvesting of sugarcane in Thailand. A mathematical model related to the problem of routing of vehicle was formulated. Harvest sequences, routes, harvesting period and harvesting time were successfully determined.

varieties; increase production of first and second generation ethanol; obtain improvement of the environmental integrated production and recycling management; develop new technologies applied to the sugarcane culture; obtain more efficient machines to planting and harvesting of sugarcane; improve vehicles and improve job qualification and many others. Other researchers from universities have established partnership with private companies in the sugar, ethanol and energy sector, aiming to solve the logistical problems, mainly focused on harvesting logistics. The transition from manual harvesting to mechanized harvesting promoted many productive gains and reduced losses; on the other hand, the harvesting system demanded a more complex planning, necessitating the development and application of mathematical and computational techniques, aiming to assist managers to make more assertive decisions during this

Mathematical Optimization Models in the Sugarcane Harvesting Process

http://dx.doi.org/10.5772/intechopen.71530

We wish to thank FAPESP (Grant No. 2009/15098-0 and 2014/01604-0), FUNDUNESP, CNPq

and Helenice de Oliveira Florentino2

\*

217

(302454/2016-0), CAPES and PROPE/PROPG UNESP for their financial support.

, Carlos Alexandre Costa Crusciol<sup>1</sup>

Research. 2016;**252**(3):969-984. DOI: 10.1016/j.ejor.2016.01.043

2 Department of Biostatistics IB, São Paulo State University, Botucatu, São Paulo, Brazil

[1] Peloia PR, Milan M, Romanelli TL.Capacity of the mechanical harvesting process of sugarcane billets. Scientia Agricola. 2010;**67**(6):619-623. DOI: 10.1590/S0103-90162010000600001

[2] Sethanan K, Neungmatcha W. Multi-objective particle swarm optimization for mechanical harvester route planning of sugarcane field operations. European Journal of Operation

[3] Ramos RP, Isler PR, Florentino HO, Jones D, Nervis JJ.An optimization model for the combined planning and harvesting of sugarcane with maturity considerations. African Journal

[4] Higgins A. Scheduling of road vehicles in sugarcane transport: A case study at an Australian sugar mill. European Journal of Operation Research. 2006;**170**(3):987-1000. DOI: 10.1016/j.

of Agricultural Research. 2016;**11**(40):3950-3958. DOI: 10.5897/AJAR2016.11441

\*Address all correspondence to: helenice@ibb.unesp.br

1 FCA, São Paulo State University, Botucatu, São Paulo, Brazil

agricultural planning.

**Acknowledgements**

**Author details**

Fernando Doriguel1

**References**

ejor.2004.07.055

In 2016, Ramos et al. [3] proposed a methodology to determine an optimum planning for planting and harvesting of the sugarcane for 5 years. The main decisions approached in this methodology are related to the determination of the planting date, selection of the varieties to be planted and determination of the harvest date for each plot, aiming to optimize the global production. A binary nonlinear optimization model was proposed and solved using computational and mathematical strategies, ensuring that the date of harvest is always in the maximum maturation period of sugarcane and considering all operational constraints of the mill. An optimal planning was determined, obtaining a potential improvement production of sugarcane 17.8% above the production obtained by conventional means.

In 2017, Junqueira and Morabito [55] proposed an optimization approach to support decisions from the scheduling and sequencing of harvesting fronts using the General Lot Sizing and Scheduling Problem (GLSPPL). Santoro et al. [56] proposed a mathematical model to solve the route planning problem of the sugarcane harvester, which aimed to optimize the time of maneuver of the harvesters in comparison to the maneuvers that were being commonly used. Based on the presented results, a 32% time reduction was observed compared with the traditional harvest process for the same area when the route of the harvest machine was not planned. Florentino et al. [57] proposed a methodology to aid the planning of the sugarcane harvesting aiming to improve the sucrose production and the raw material quality, considering the constraints imposed by the mill as well as the sugarcane demand per period. In this way, an extended goal programming model was proposed to optimize sugarcane harvest planning, so that the harvesting is done as close as possible to the sugarcane maturity peak. A genetic algorithm (GA) was developed in order to solve large-size problems with an appropriate computational time. A comparative analysis between GA and an exact method for small instances was given to validate the performance of the model and the methods developed. The computational results show that crop planning for small farms can be generated by the exact method, and for medium and large farms, a metaheuristic is required for this planning.
